What does authorized against your credit card at a car rental mean?

It's probably a reference to the deposit hold put on your credit card at the time of rental. In such cases, the amount of the deposit is not actually charged to your card, but a "hold" is placed on that amount (basically, reserving that amount of money against your maximum charge limit).

For example, if your credit card limit is $5,000, and a deposit hold of $250 is put on that card, your limit becomes $4,750 during the time that hold is active, because $250 is being earmarked for the rental company in case it is needed in the future.